Page 339 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

CeII, Stack and System ModeIIing 315

issues such as the choice of heat engine and the integration of heat engine and
heat exchangers. The hardware design examines the geometric effects on the
system cost through its effects on the power density, thermal insulation, and
the wall of the pressure vessel. Such analysis provides valuable information for
design optimisation.
These and other system modelling analyses show how strongly system
characteristics such as efficiency depend on accurate input data for the
electrochemical model used in simulating stack performance. On the other hand,
these studies also show the strong effect of turbine operating parameters (e.g.,
pressure ratios and maximum allowable temperature) on the system
performance. Such studies clarify that the ultimate design of the stack and the
required accuracy of stack modelling are best determined after preliminary
system design studies have been performed using rough stack, reformer, and
turbine models.

11.7 Thermomechanical Model
Avoiding thermomechanical failure is critical to the applications of the SOFC
technology. SOFCs are produced by processing at elevated temperatures. As the
cells are cooled to room temperature, stresses due to mismatch in coefficients of
thermal expansion (CTEs) are developed. Additional residual stresses develop in
the stack during the assembly and sealing process. The factors that affect the
magnitude of the stresses include (i) differences in CTEs of the material parts, (ii)
the differentia1 between stress-free (processing) temperature and operation
temperature, (iii) elastic constants of the components, and (iv) the thickness of
the cell components. Because the cell thickness is much less than the Iateral
dimensions, the elasticity problem may be approximated as 2-D and the state of
stress is thus biaxial. For the state-of-the-art PEN materials, cathode (LSM) and
eIectrolyte (YSZ) have simiIar CTEs, while the CTE of the anode (Ni + YSZ) is
higher. Thus, when cooled from a high temperature, stresses in the electrolyte
and the cathode would tend to be compressive, while stresses in the anode would
be tensile. In an anode-supported cell, the tensile stress can cause a delamination
crack between the anode and the electrolyte.
The residual stress in a cell when cooled from stress-free temperature to room
temperature can be calculated [39]:
QI = (B2 - Pl)EIAT/[1+ hlEl/h2E21 (30)

where pis the thermal expansion coefficient, AT is the change in temperature, his
the layer thickness, and E is the biaxial modulus. The subscripts ‘1’ and ‘2’ denote
two neighbouring layers of the cell. From Eq. (30) it can be seen that thin layers
suffer higher residual stresses than thick layers. In the anode-supported cell, the
electrolyte has a much higher residual stress than the anode. Fortunately,
the electrolyte is strong against compressive stresses. For the anode, the tensile
stressisaconcern.AssumingAT= lOOOI<, p2- = 1.7 x 10-6/”C,E2=200GPa,